3 Answers
3

Nearly drowned means you almost died by means of drowning, but did not drown. This means you survived.Nearly rescued means you almost were saved by a third-party, but were not saved. This means you are still being affected by the situation (in this case, drowning to death).

The riddle hinges on this distinction. It's better to almost die but not die, than to be almost saved from dying but still die.

Note that people sometimes confuse "near(ly)" with "narrow(ly)". If you narrowly drowned, you were nearly rescued (= you drowned). If you were narrowly rescued, you nearly drowned (= you were rescued).
– FlaterFeb 8 at 8:27

If you were "nearly drowned" you just avoided drowning, by implication you were probably rescued. If you were "nearly rescued" then someone tried to rescue you but just failed. By implication you drowned!

There is another, rather dated and much less frequently used meaning of "nearly" which is "only just". The joke in the riddle is, presumably, based on this double meaning. The question could then be taken to mean "Would you rather be almost drowned or almost rescued" or "Would you rather be only just drowned or only just rescued".

Presumably the person who asked the riddle would, whatever answer was given, then say, something like "Oh, you'd rather be dead then". It's not a very funny joke but it could be from an old book, most Victorian humour seems pretty strange to 21st century people.

"most Victorian humour seems pretty strange to 21st century people" I wonder what people few centuries after us would be talking about. "Yes, 21st century people had this strange humour based on images with text overlaid on them."
– VLAZFeb 8 at 12:52

@vlaz Of course, most humour generally dates very quickly. Even the most accessible stuff like Three Men in a Boat, The Diary of a Nobody and The Importance of Being Earnest isn't as funny now as it used to be. I think it's a combination of the change of language and, probably more importantly, the changes in the social background that mean that a lot of the references don't have the immediate resonance.
– BoldBenFeb 9 at 12:14